Size quantization in semiconductors

It is generally assumed that the electronic properties of a semicondnctor are independent of crystal size. However, recent studies have shown that if the particle size of the semiconductor is less than approximately 10 nm, then many of their physicochemical properties appear to be substantially different from analogous properties of a bulk material. This is because the electrons and holes are confined in the region of space defined by potential barriers that are comparable to or smaller than their respective de Broglie wavelengths so that allowed energy states become discrete (or quantized). This effect is referred to as the size quantization effect (SQE) or the quantum size effect. SQE is also observed in the noble metals (4). Eor semiconductors, the critical dimension for SQE depends upon the effective masses of the electrons () and the holes (m ). For example, for m 0.05, the critical dimension is approximately 30 mn. Thus, for semiconductors, SQE is observed in 

Two models have been used to explain SQE in the case of semiconductor nanoparticles. The first model is an effective mass approximation (6-11) developed for relatively larger particles. The second model assumes a tight-binding framework for well-defined small 

The dashed curves are the results of the effective mass approximation, (b) Similar results for ZnS cluster. 3.7 eV(+). Reprinted with permission from reference (12). Copyright 1989 by 

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However, there are a number of difficulties associated with the synthesis of colloidal semiconductor particles. The preparation of stable, monodispersed, well-characterized populations of nanosized, colloidal semiconductor particles is experimentally demanding and intellectually challenging. Small and uniform particles are needed to diminish non-productive electron-hole recombinations the mean distance by which the charge carriers need to diffuse to reach the particle surface from which they are released is necessarily reduced in small particles. Monodispersity is a requirement for the observation of many of the spectroscopic and electro-optical manifestations of size quantization in semiconductor particles. Small semiconductor particles are difficult to maintain in solution in the absence of stabilizers flocculations and Ostwald ripening... 

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